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Share-Based Compensation - Non-Cash Expense (Details) - USD ($)
$ in Thousands
3 Months Ended
Mar. 31, 2021
Mar. 31, 2020
Share-Based Compensation    
Share-based compensation expense $ 48,726 $ 16,879
Less: Share-based compensation expense attributable to non-controlling interests 360 0
Share-based compensation expense attributable to Biohaven Pharmaceutical Holding Company Ltd. $ 48,366 16,879
Minimum    
Share-Based Compensation    
Requisite service period of award (in years) 3 years  
Maximum    
Share-Based Compensation    
Requisite service period of award (in years) 4 years  
Research and development expenses    
Share-Based Compensation    
Share-based compensation expense $ 20,058 6,251
Selling, general and administrative expenses    
Share-Based Compensation    
Share-based compensation expense $ 28,668 $ 10,628